IEEE Transactions on Pattern Analysis and Machine Intelligence
Sketch based coding of grey level images
Signal Processing
Computation of stereo disparity using regularization
Pattern Recognition Letters
Multiresolution elastic matching
Computer Vision, Graphics, and Image Processing
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Characterization of Signals from Multiscale Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
Comparing methods of interpolation for scattered volumetric data
State of the art in computer graphics
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JPEG 2000: Image Compression Fundamentals, Standards and Practice
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JPEG Still Image Data Compression Standard
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Smart Interpolation by Anisotropic Diffusion
ICIAP '03 Proceedings of the 12th International Conference on Image Analysis and Processing
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adapted Total Variation for Artifact Free Decompression of JPEG Images
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Image compression by linear splines over adaptive triangulations
Signal Processing
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Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
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Journal of Mathematical Imaging and Vision
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Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Vector-valued image interpolation by an anisotropic diffusion-projection PDE
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
On image reconstruction from multiscale top points
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Towards PDE-Based image compression
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
IEEE Transactions on Information Theory
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
An axiomatic approach to image interpolation
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Morse description and geometric encoding of digital elevation maps
IEEE Transactions on Image Processing
Image up-sampling using total-variation regularization with a new observation model
IEEE Transactions on Image Processing
Image Compression With Edge-Based Inpainting
IEEE Transactions on Circuits and Systems for Video Technology
Special Issue on Tribute Workshop for Peter Johansen
Journal of Mathematical Imaging and Vision
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Beating the Quality of JPEG 2000 with Anisotropic Diffusion
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Invariant image reconstruction from irregular samples and hexagonal grid splines
Image and Vision Computing
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Proceedings of the 32nd DAGM conference on Pattern recognition
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Calcolo: a quarterly on numerical analysis and theory of computation
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Journal of Mathematical Imaging and Vision
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CCIW'11 Proceedings of the Third international conference on Computational color imaging
Edge-based compression of cartoon-like images with homogeneous diffusion
Pattern Recognition
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
Partial differential equations for interpolation and compression of surfaces
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Optimising spatial and tonal data for homogeneous diffusion inpainting
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
On the impact of anisotropic diffusion on edge detection
Pattern Recognition
On-chip semidense representation map for dense visual features driven by attention processes
Journal of Real-Time Image Processing
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Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec.